A set of data is normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a randomly selected data point will be between 85 and 115?

Step 1 ：Step 1: We first need to convert the given data points to z-scores. The formula for finding the z-score is $z=\frac{x-\mu }{\sigma }$, where $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step 2 ：Step 2: For 85, the z-score is $z=\frac{85-100}{15}=-1$. For 115, the z-score is $z=\frac{115-100}{15}=1$.

Step 3 ：Step 3: We then use the standard normal distribution table to find the probability for the given z-scores. The probability for z = -1 is 0.1587 and the probability for z = 1 is 0.8413.

Step 4 ：Step 4: The probability that the data point is between 85 and 115 is the difference between the probabilities of the two z-scores, which is $0.8413-0.1587=0.6826$.